IDENTIFICATION OF CONCEALED LITHOLOGIES FROM DISPARATE DATA LAYERS USING USING POSSIBILITY THEORY

As part of the U. S. Geological Survey's Assessment Techniques for Concealed Mineral Resources Project, possibility theory has been evaluated as a method for identification of buried lithologies by comparison with the possibility distributions of measures of nearby exposed "candidate terranes". Possibility theory is a general theory of the possibility of occurrence of events in the presence of both uncertainty and less than complete knowledge. The possibility of an event is a continuous variable between zero and one rather than a binary off or on as in probability. Thus, any geologic variables, such as degree of fracturing or percentage of a particular lithology in a formation, can be represented. Probability theory is a subset of possibility theory where the possibility function has only nonzero values at zero (not present) and one (present with absolute certainty). Because of this, probability theory cannot distinguish the case of total lack of knowledge from certainty, whereas possibility theory is able to make the distinction. Possibility functions based on quantitative data, for example, a histogram of anomaly amplitudes, are directly computed from the appropriate mathematical transformation and thus are objective. Possibility functions based on qualitative, linguistic, or subjective data are quantified by simple rules with uncertainties reflecting both the variability of the property and the degree of knowledge of that property. Estimates from possibility theory are conservative and automatically include uncertainty in the criteria estimates; moreover, they overcome the sharp boundary problem of interval analysis. The theory allows logical combinations of the possibility functions for quantitative, semi-quantitative, and qualitative measures; thus many disparate data types can be utilized in the decision process. For quantitative areal data (for example, aeromagnetic, gravity and electromagnetic surveys), measures within the target and candidate areas that have been used include the distributions within a moving window of: anomaly amplitudes; total number of extrema; elongation ratio (peaks or troughs/all extrema); maximum curvature strike and strike standard deviation; and anomaly surface area. All of these measures contribute useful information for identifying terrane lithology and at least in the study area coincidentally identified some ordering of tectonic events. For semi-quantitative and qualitative (subjective) data, geological map and structural interpretations, trends and distributions of geochemical data, and mineral resource occurrence are used to contour possibility in a spatial (map) distribution. Logical combinations of the various measures (for example, "A and B and C or D not E") determines a final possibility distribution for each candidate terrane (for example, Figure 1). These distributions determine the overall ranking of the candidate lithologies for the target area. Two examples over covered targets in the Santa Cruz Valley in southeastern Arizona unambiguously identified the targets as intrusive diorite in one case and Tertiary volcanic flows in the other. Combining qualtitative geologic, mineral occurrence, and geochemical data with the quantitative geophysical data allows a quantified prospectivity estimate (Figure 2).